Question

a spinner is divided into 5 sections of equal size. you spin it 4 times, with the following results: 1, 5, 3, 2. which of the following is false?
a. the theoretical probability of a 1 is 20%. c. if you spin the spinner again and get different results, the theoretical probability will change.
b. the experimental probability of a 2 is 25%. d. all of the above are true.
please select the best answer from the choices provided

Explanation:

Step1: Calculate theoretical probability

The spinner has 5 equal - sized sections. The theoretical probability \(P\) of landing on any one section is \(P=\frac{1}{5}=0.2 = 20\%\). So, the theoretical probability of a 1 is \(20\%\), and statement a is true.

Step2: Calculate experimental probability

The experimental probability \(P_{exp}\) is calculated as \(P_{exp}=\frac{\text{number of times the event occurs}}{\text{total number of trials}}\). The number of trials \(n = 4\), and the number of times 2 occurs \(m = 1\). So, \(P_{exp}=\frac{1}{4}=0.25=25\%\), and statement b is true.

Step3: Analyze the nature of theoretical probability

The theoretical probability is based on the structure of the spinner (number of equal - sized sections). It does not change with the results of additional spins. So, statement c is false.

Answer:

C. If you spin the spinner again and get different results, the theoretical probability will change.